Aircraft: WIDEBODY; LOW WING; 2 TURBOJET ENG
Phase of flight: Initial Approach
Anomaly: ATC Issue All Types; Deviation - Altitude Excursion From Assigned Altitude; Deviation - Altitude Undershoot; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy; Flight Deck / Cabin / Aircraft Event Illness / Injury

We were on the SSCOT THREE RNAV arrival inside of WALIP leveled off at 3;000. I was the Pilot Flying (PF) using LNAV and VNAV when given the RNAV GPS [Runway] 8L at MIA. The Captain (CA) was attempting to clean up the FMC as it had the next waypoint behind us instead of in front of us (incorrect routing and mileage was showing) which was due to my reselecting both the runway and SSCOT arrival. (I should have only selected the new change of runway.) Approximately 15-18 miles from the runway the controller said he showed us at 2;300 feet. While we had 3;000 feet showing in the MCP window; we had in fact descended. I was unclear as to why the aircraft left 3;000 feet as I had been in VNAV path along with LNAV. I disconnected the AP so as to try to regain the 3000 as smoothly as I could without being abrupt. Once we recaptured the altitude; I reengaged the AP and immediately lowered the gear thinking we were over VICUV which slowed up the airspeed. (We were in and out of IMC buildups but had visual with the field about 5 -7miles from the runway.) Once we were actually at VICUV; I had regained airspeed and called for rest of flaps so as to be fully configured and stable by 1;000 feet. I made my 'stable' call out at 1000 while CA made his at 500 feet and landed uneventfully runway 8L. In our scenario; I do not need to reselect the arrival along with the runway as this caused the CA to be heads down cleaning up the legs page. I had lost my Situational Awareness between WALIP and VICUV due to the mileage reading incorrectly. I should have KEPT verifying on the FMA that we were in VNAV PTH so as not to start an early descent. In the future; I will more carefully reselect the new rwy approach when given a change of runway. I will also ensure on the FMA that I am continuously in either VNAV PTH or ALT HOLD. Entire flight proceeded normally. We briefed the Runway 9 ILS shortly before leaving cruise. Typically; ATC assigns 9 to aircraft coming over the Gulf of Mexico. I was the pilot monitoring and contacted MIA Approach as we were crossing SSCOT Waypoint at 10;000 feet; 250 knots. The controller cleared us to descend to 8000 ft and assigned us the RNAV (GPS) 8L approach. This was where everything turned into a mess; I don't recall a heading assignment; but later saw 121 heading on the MCP. When we received the approach assignment; the First Officer (FO) proceeded to change the FMS to the new approach. I said to the FO; 'You got it?' The FO said yes. I said I'll pull up the chart. My iPad was blanked out; so I pushed the button to bring it up again. Login Page! Typed in the code. Damn! In the descent from cruise; the Fight Attendants had called to report a passenger had vomited all over the right mid lav. I had left the Jepp pages to send in the maintenance code. I would write it up at the gate. Ok. Now back to Jepps pages. There's ILS 9. Touch to pull up charts. Favorites! RNAV 8L is not a favorite. Touch to pull all charts. Scroll down. Scroll down. Scroll down. Touch. No! Not that runway! Back. Touch. Got it! '[Aircraft X] descend and maintain 3000.' 'Descend an maintain 3000; [Aircraft X].' I don't remember; but I think I was on the 20 mile scale of the ND. WALIP; LECIT; VICUV; and KACDE were displayed. The FMS is still on the legs page; now showing WALIP; LECIT; vectors VICUV; KACDE. 8L on the next page. Back one page. I tell the FO it's in there and I'll extend it out of VICUV. [Aircraft X] join the final approach to 8L. Roger [Aircraft X] join the final to 8L. I look at our heading selection and it says 121 and; as I said earlier; I didn't recall getting a heading clearance and we weren't tracking anything. Approach we're having some trouble setting up the approach; do you have a heading you want [Aircraft X] to fly to join? Fly heading 110. I return to the box to extend from VICUV. This is the FMS that does not use a Direct Intercept key. I put VICUV at the top of the page; but it wouldn't get an intercept course. The FMS said DISCONTINUITY. The FO pointed it out as well. '[Aircraft X] you are south of course. Turn left to 060 heading to join the 8L final approach course. Maintain 3000 feet.' 'Roger [Aircraft X] come left to 060 to join the localizer uh final approach course.' I asked the FO to pull up the localizer and join it while I kept working the magic. The FO said I'm going to start slowing down. Below 250 flaps one. Verified. Flaps going to one. Flight attendants prepare for landing. The FO said Gear down. OK. Gear down. Somewhere in the middle of; I thought to push the legs key again; the first time since before passing SSCOT. There were a whole load of waypoints all the way back into the Gulf. From the FO's training for preflight route upload; the FO entered the RNAV 8L approach; SSCOT 3 arrival and transition. Although my LEGS page in the FMS was still where I was using it; it was no longer the FIRST LEGS page. [Aircraft X] you are now north of course. Turn right to 110 heading to join the 8L final approach course. Roger right to 110 heading to join the 8L localizer; uh 8L final approach course.[Aircraft X]. The FO said I'm turning the autopilot off. OK Flaps to 5. OK Verified below 230. Flaps 5. OK I've got you extended out of VICUV. How's it look? [Aircraft X] I show you at 2400 feet; your clearance is to cross VICUV at 3000 feet. Well; isn't that special. I showed 2200 feet; but we weren't really climbing yet. I said; Come on; Let's get back up to three. And let's get the autopilot back on. We're supposed to use the autopilot on VNAV approaches; right? I'm sure there was more confusion in there; but my ASAP might time-out. Read it fast. That's how it was going.Well; I could have simplified my life if I had requested the Localizer 8L. It wasn't OTS. Tuning a localizer is much quicker and simpler than programming a computer. Years ago; in the beginning of these RNAV approaches at LAX; controllers would change runways closer in on the arrival and things were getting messed up all over Riverside. After lots of ASAP reports; controllers policies only allowed them to change up the runway much further out; unless it was a visual to join the other localizer. Basically; they won't change your runway assignment if you're inside the runway transition. Of course; I could have requested direct to VICUV and we could have at least pointed to it; then figured out the problem with the FMS without S turning all over the Everglades. Frankly; if controllers have a working localizer to a runway; I think they ought to use it. A widebody crew on approach to MIA Runway 9 described the confusion and work overload after ATC assigned the RNAV GPS 8L from the previously briefed Runway 9 ILS. The close in approach change required iPad activation; FMS programming and heavy crew activity resulting in track deviations and an eight hundred foot altitude excursion.